TITLE:
Existence of Random Attractor Family for a Class of Nonlinear Higher-Order Kirchhoff Equations
AUTHORS:
Guoguang Lin, Changqing Zhu
KEYWORDS:
Stochastic Dynamical Systems, Random Attractor Family, White Noise, Ornstein-Uhlenbeck Process, Tempered Sets
JOURNAL NAME:
International Journal of Modern Nonlinear Theory and Application,
Vol.8 No.2,
April
23,
2019
ABSTRACT: The existence of random attractor family for a class of nonlinear nonlocal higher-order Kirchhoff partial differential equations with additive white noise is studied. The weak solution of the equation is established by the Ornstein-Uhlenbeck process to deal with the random term, and a bounded random absorption set is obtained. And then, the existence of the random attractor family is proved by the isomorphism mapping method.